Question

1 If sum and product of zeroes of quadratic
polynomial are, respectively 8 and 12, then find
their zeroes.
CBSE​

Answer 1

Given

Sum of zeroes = 8

Product of zeroes = 12

To find

Zeroes of quadratic polynomial

We have

α + β = 8 and αβ = 12

General equation

x² - (α+β)x + αβ = 0

Put the value , we get

x² - 8x + 12 = 0

Now Take

x² - 8x + 12 = 0

Using middle term splitting , we get

x² - 6x - 2x + 12 = 0

x(x - 6) - 2(x - 6) = 0

(x - 6)(x - 2) = 0

x = 6 and x = 2

Answer

zeroes are 6 and 2  

Answer 2

Answer:

Given :-

• Sum and product of zeroes of quadratic polynomial and 8 and 12 respectively.

To Find :-

• What is their zeroes.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{{x}^{2} - (Sum\: of\: zeroes)x + Product\: of\: zeroes =\: 0}}}$

Solution :-

Given :

• Sum of zeroes = 8
• Product of zeroes = 12

According to the question by using the formula we get,

$\implies \sf {x}^{2} - (8)x + 12 =\: 0$

$\implies \sf {x}^{2} - 8x + 12 =\: 0$

$\implies \sf {x}^{2} - (6 + 2)x + 12 =\: 0$

$\implies \sf {x}^{2} - 6x - 2x + 12 =\: 0$

$\implies \sf x(x - 6) - 2(x - 6) =\: 0$

$\implies \sf (x - 6) (x - 2) =\: 0$

$\implies \sf (x - 6) =\: 0$

$\implies \sf\bold{\red{x =\: 6}}$

Either,

$\implies \sf (x - 2) =\: 0$

$\implies \sf\bold{\red{x =\: 2}}$

$\therefore$ The zeroes of the quadratic polynomial is 6 and 2 .